Note that the relevant aspect of the KL property is when \(\Omega \)  is a subset of critical points for \(\psi \) , i.e., \(\Omega \subseteq \lbrace x: \nabla \psi (x)=0 \rbrace \) . The KL property holds for semi-algebraic functions (e.g., real polynomial functions), vector or matrix (semi)norms (e.g., \(\Vert \cdot \Vert _p\)  with \(p \ge 0\)  rational number), logarithm functions, exponential functions and uniformly convex functions, see [1]} for a comprehensive list.
